{
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "# Range SLAM with Batch Optimization\n",
        "\n",
        "A 2D Range SLAM example using batch optimization (Levenberg-Marquardt) on the Plaza2 dataset.\n",
        "\n",
        "This notebook mirrors the functionality of the MATLAB batch SLAM script, adapted using Python and GTSAM, drawing structural elements from the iSAM example.\n",
        "\n",
        "Author: Frank Dellaert (adapted for batch by AI)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "id": "colab_import",
      "metadata": {
        "tags": [
          "remove-cell"
        ]
      },
      "outputs": [],
      "source": [
        "try:\n    import google.colab\n    %pip install --quiet gtsam-develop\nexcept ImportError:\n    pass"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "<a href=\"https://colab.research.google.com/github/borglab/gtsam/blob/develop/python/gtsam/examples/RangeSLAMExample_plaza2.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "tags": [
          "remove-cell"
        ]
      },
      "source": [
        "GTSAM Copyright 2010-2022, Georgia Tech Research Corporation,\n",
        "Atlanta, Georgia 30332-0415\n",
        "All Rights Reserved\n",
        "\n",
        "Authors: Frank Dellaert, et al. (see THANKS for the full author list)\n",
        "\n",
        "See LICENSE for the license information"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "Data is second UWB ranging dataset, B2 or \"plaza 2\", from\n",
        "\n",
        "> \"Navigating with Ranging Radios: Five Data Sets with Ground Truth\", by Joseph Djugash, Bradley Hamner, and Stephan Roth, available at https://www.ri.cmu.edu/pub_files/2009/9/Final_5datasetsRangingRadios.pdf\n",
        "\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 21,
      "metadata": {
        "tags": [
          "remove-cell"
        ],
        "vscode": {
          "languageId": "markdown"
        }
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "\u001b[31mERROR: Could not find a version that satisfies the requirement gtsam-develop (from versions: none)\u001b[0m\u001b[31m\n",
            "\u001b[0m\u001b[31mERROR: No matching distribution found for gtsam-develop\u001b[0m\u001b[31m\n",
            "\u001b[0mNote: you may need to restart the kernel to use updated packages.\n"
          ]
        }
      ],
      "source": [
        "%pip install --quiet gtsam-develop"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 34,
      "metadata": {},
      "outputs": [],
      "source": [
        "# pylint: disable=invalid-name, E1101\n",
        "\n",
        "import gtsam\n",
        "from gtsam import Point2, Pose2, symbol\n",
        "import numpy as np\n",
        "import math\n",
        "import time \n",
        "import plotly.express as px\n",
        "\n",
        "from gtsam.utils import plot # Needs matplotlib\n",
        "from numpy.random import default_rng\n",
        "\n",
        "rng = default_rng()\n",
        "\n",
        "NM = gtsam.noiseModel"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "## Load Data"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 35,
      "metadata": {},
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "Read 4090 odometry entries.\n"
          ]
        }
      ],
      "source": [
        "# load the odometry\n",
        "# DR: Odometry Input (delta distance traveled and delta heading change)\n",
        "#    Time (sec)  Delta Distance Traveled (m) Delta Heading (rad)\n",
        "odometry_data = {}\n",
        "data_file_dr = gtsam.findExampleDataFile(\"Plaza2_DR.txt\")\n",
        "odo_times_list = []\n",
        "for row in np.loadtxt(data_file_dr):\n",
        "    t, distance_traveled, delta_heading = row\n",
        "    odometry_data[t] = Pose2(distance_traveled, 0, delta_heading)\n",
        "    odo_times_list.append(t)\n",
        "\n",
        "odo_times_list.sort() # Ensure times are sorted\n",
        "M = len(odometry_data)\n",
        "print(f\"Read {M} odometry entries.\")"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 36,
      "metadata": {},
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "Read 1816 range triples for 4 unique landmarks.\n"
          ]
        }
      ],
      "source": [
        "# load the ranges from TD\n",
        "#    Time (sec)  Sender / Antenna ID Receiver Node ID  Range (m)\n",
        "triples = []\n",
        "landmark_ids = set()\n",
        "data_file_td = gtsam.findExampleDataFile(\"Plaza2_TD.txt\")\n",
        "for row in np.loadtxt(data_file_td):\n",
        "    t, sender, receiver, _range = row\n",
        "    landmark_id = int(receiver)\n",
        "    triples.append((t, landmark_id, _range))\n",
        "    landmark_ids.add(landmark_id)\n",
        "\n",
        "K = len(triples)\n",
        "sorted_landmark_ids = sorted(list(landmark_ids))\n",
        "print(f\"Read {K} range triples for {len(landmark_ids)} unique landmarks.\")"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "## Set Parameters and Noise Models"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 37,
      "metadata": {},
      "outputs": [],
      "source": [
        "# parameters\n",
        "sigmaR = 50        # range standard deviation (matches MATLAB)\n",
        "sigmaInitialLandmark = 1.0 # Stddev for random landmark init (matches MATLAB)\n",
        "robust = True"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 38,
      "metadata": {},
      "outputs": [],
      "source": [
        "# Set Noise parameters (mirrors MATLAB script)\n",
        "priorSigmas = gtsam.Point3(1, 1, math.pi)  # Prior on Pose 0\n",
        "pointPriorSigmas = gtsam.Point2(1, 1) # Loose prior on landmarks\n",
        "odoSigmas = gtsam.Point3(0.05, 0.01, 0.2) # Odometry noise\n",
        "\n",
        "priorNoise = NM.Diagonal.Sigmas(priorSigmas) # prior on pose 0\n",
        "pointPriorNoise = NM.Diagonal.Sigmas(pointPriorSigmas) # loose LM prior\n",
        "odoNoise = NM.Diagonal.Sigmas(odoSigmas)     # odometry\n",
        "\n",
        "# Range noise\n",
        "gaussian = NM.Isotropic.Sigma(1, sigmaR)     # non-robust\n",
        "base = NM.mEstimator.Tukey(15) # Tukey M-estimator like MATLAB\n",
        "tukey = NM.Robust.Create(base, gaussian)  # robust\n",
        "rangeNoise = tukey if robust else gaussian"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "## Build Factor Graph and Initial Estimate"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 39,
      "metadata": {},
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "Initializing Landmarks...\n",
            "Initialized 4 landmarks.\n"
          ]
        }
      ],
      "source": [
        "# Initialize Factor Graph and Initial Values\n",
        "graph = gtsam.NonlinearFactorGraph()\n",
        "initial = gtsam.Values()\n",
        "\n",
        "# Add prior on first pose\n",
        "# Estimate pose0 from the first odometry time's neighborhood or use a fixed reasonable guess.\n",
        "# Using the same value as the iSAM example for consistency.\n",
        "pose0 = Pose2(-34.2086489999201, 45.3007639991120, math.pi - 2.021089)\n",
        "graph.add(gtsam.PriorFactorPose2(0, pose0, priorNoise))\n",
        "initial.insert(0, pose0)\n",
        "\n",
        "# Initialize Landmarks (similar to MATLAB approach)\n",
        "print(\"Initializing Landmarks...\")\n",
        "for j in sorted_landmark_ids:\n",
        "    landmark_key = symbol('L', j)\n",
        "    # Initialize randomly around origin (adjust scale if needed)\n",
        "    initial_point = Point2(sigmaInitialLandmark * rng.normal(), sigmaInitialLandmark * rng.normal())\n",
        "    initial.insert(landmark_key, initial_point)\n",
        "    # Optional: Add a loose prior to help localization if landmarks are poorly constrained\n",
        "    # graph.add(gtsam.PriorFactorPoint2(landmark_key, Point2(0,0), pointPriorNoise))\n",
        "print(f\"Initialized {len(sorted_landmark_ids)} landmarks.\")"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 40,
      "metadata": {},
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "\n",
            "Building Pose Chain and Odometry Factors...\n",
            "Added 4090 odometry factors and initial pose estimates.\n"
          ]
        }
      ],
      "source": [
        "print(\"\\nBuilding Pose Chain and Odometry Factors...\")\n",
        "lastPose = pose0\n",
        "pose_times = [odo_times_list[0]] # Approximate time for pose 0\n",
        "# Loop over odometry measurements\n",
        "for i, t in enumerate(odo_times_list, 1):\n",
        "    # get odometry measurement for this time step\n",
        "    odometry = odometry_data[t]\n",
        "\n",
        "    # add odometry factor\n",
        "    graph.add(gtsam.BetweenFactorPose2(i - 1, i, odometry, odoNoise))\n",
        "\n",
        "    # predict pose and add as initial estimate\n",
        "    predictedPose = lastPose.compose(odometry)\n",
        "    lastPose = predictedPose\n",
        "    initial.insert(i, predictedPose)\n",
        "    pose_times.append(t)\n",
        "\n",
        "print(f\"Added {M} odometry factors and initial pose estimates.\")"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 41,
      "metadata": {},
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "\n",
            "Adding Range Factors...\n",
            "Added 1816 range factors.\n"
          ]
        }
      ],
      "source": [
        "print(\"\\nAdding Range Factors...\")\n",
        "# Convert pose_times to numpy array for efficient search\n",
        "pose_times_np = np.array(pose_times)\n",
        "\n",
        "# Add range factors\n",
        "range_factors_added = 0\n",
        "for t_range, landmark_id, measured_range in triples:\n",
        "    # Find the pose index active at the time of the range measurement\n",
        "    # Get the index of the *last* pose time that is <= t_range\n",
        "    pose_index = np.searchsorted(pose_times_np, t_range, side='right') - 1\n",
        "    \n",
        "    # Ensure pose_index is valid (it might be -1 if t_range is before the first odometry time)\n",
        "    if pose_index < 0:\n",
        "        # print(f\"Warning: Range measurement at time {t_range} is before the first pose time {pose_times_np[0]}. Skipping.\")\n",
        "        pose_index = 0 # Or skip the measurement\n",
        "\n",
        "    landmark_key = symbol('L', landmark_id)\n",
        "    graph.add(gtsam.RangeFactor2D(pose_index, landmark_key, measured_range, rangeNoise))\n",
        "    range_factors_added += 1\n",
        "\n",
        "print(f\"Added {range_factors_added} range factors.\")"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "## Optimize the Factor Graph"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 42,
      "metadata": {},
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "\n",
            "Optimizing the factor graph...\n",
            "Initial error: 2.9e+02, values: 4095\n",
            "iter      cost      cost_change    lambda  success iter_time\n",
            "   0      1.4e+05     -1.4e+05      1e-05      1       0.03\n",
            "iter      cost      cost_change    lambda  success iter_time\n",
            "   0      9.1e+03     -8.8e+03     0.0001      1       0.03\n",
            "iter      cost      cost_change    lambda  success iter_time\n",
            "   0      1.9e+02        1e+02      0.001      1       0.03\n",
            "   1      2.7e+03     -2.5e+03     0.0001      1       0.03\n",
            "   1      1.1e+02           86      0.001      1       0.02\n",
            "   2      1.7e+03     -1.6e+03     0.0001      1       0.02\n",
            "   2           85           22      0.001      1       0.03\n",
            "   3      6.3e+02     -5.5e+02     0.0001      1       0.03\n",
            "   3           76          8.4      0.001      1       0.02\n",
            "   4      3.1e+02     -2.3e+02     0.0001      1       0.02\n",
            "   4           68          8.6      0.001      1       0.03\n",
            "   5      1.9e+02     -1.2e+02     0.0001      1       0.03\n",
            "   5           55           13      0.001      1       0.03\n",
            "   6      2.6e+02       -2e+02     0.0001      1       0.02\n",
            "   6           39           16      0.001      1       0.02\n",
            "   7      1.4e+02          -99     0.0001      1       0.04\n",
            "   7           26           13      0.001      1       0.03\n",
            "   8           94          -68     0.0001      1       0.03\n",
            "   8           21          5.5      0.001      1       0.03\n",
            "   9           63          -43     0.0001      1       0.02\n",
            "   9           19          2.1      0.001      1       0.02\n",
            "  10           46          -27     0.0001      1       0.02\n",
            "  10           17          1.8      0.001      1       0.03\n",
            "  11           35          -18     0.0001      1       0.03\n",
            "  11           15          1.5      0.001      1       0.03\n",
            "  12           27          -12     0.0001      1       0.03\n",
            "  12           14          1.3      0.001      1       0.02\n",
            "  13           22         -7.9     0.0001      1       0.02\n",
            "  13           13          1.2      0.001      1       0.03\n",
            "  14           18         -5.2     0.0001      1       0.03\n",
            "  14           12            1      0.001      1       0.03\n",
            "  15           15         -3.3     0.0001      1       0.03\n",
            "  15           11          0.9      0.001      1       0.02\n",
            "  16           13           -2     0.0001      1       0.02\n",
            "  16           10         0.79      0.001      1       0.04\n",
            "  17           11         -1.1     0.0001      1       0.03\n",
            "  17          9.3          0.7      0.001      1       0.03\n",
            "  18          9.8        -0.44     0.0001      1       0.03\n",
            "  18          8.7         0.62      0.001      1       0.02\n",
            "  19          8.7        0.023     0.0001      1       0.02\n",
            "  20           67          -58      1e-05      1       0.02\n",
            "  20            5          3.7     0.0001      1       0.03\n",
            "  21           23          -18      1e-05      1       0.03\n",
            "  21          3.5          1.4     0.0001      1       0.03\n",
            "  22          9.4         -5.9      1e-05      1       0.03\n",
            "  22            3         0.57     0.0001      1       0.03\n",
            "  23            5           -2      1e-05      1       0.03\n",
            "  23          2.6         0.34     0.0001      1       0.02\n",
            "  24          3.3        -0.71      1e-05      1       0.02\n",
            "  24          2.4         0.26     0.0001      1       0.03\n",
            "  25          2.6        -0.19      1e-05      1       0.03\n",
            "  25          2.2         0.21     0.0001      1       0.03\n",
            "  26          2.1        0.034      1e-05      1       0.03\n",
            "  27          3.7         -1.5      1e-06      1       0.03\n",
            "  27          1.1            1      1e-05      1       0.02\n",
            "  28          1.4        -0.24      1e-06      1       0.04\n",
            "  28         0.93          0.2      1e-05      1       0.03\n",
            "  29         0.96       -0.031      1e-06      1       0.04\n",
            "  29         0.88        0.048      1e-05      1       0.09\n",
            "  30         0.88      0.00063      1e-06      1       0.03\n",
            "Optimization complete in 1.93 seconds.\n",
            "Initial Error: 294.2927831483431\n",
            "Final Error: 0.8771120075818397\n"
          ]
        }
      ],
      "source": [
        "# Graph built, optimize!\n",
        "print(\"\\nOptimizing the factor graph...\")\n",
        "start_time = time.time()\n",
        "\n",
        "params = gtsam.LevenbergMarquardtParams()\n",
        "params.setRelativeErrorTol(1e-3) # Convergence tolerance\n",
        "params.setVerbosityLM(\"SUMMARY\") # Print LM progress\n",
        "optimizer = gtsam.LevenbergMarquardtOptimizer(graph, initial, params)\n",
        "result = optimizer.optimize()\n",
        "\n",
        "end_time = time.time()\n",
        "print(f\"Optimization complete in {end_time - start_time:.2f} seconds.\")\n",
        "\n",
        "print(f\"Initial Error: {graph.error(initial)}\")\n",
        "print(f\"Final Error: {graph.error(result)}\")"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "## Print and Visualize Results"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 43,
      "metadata": {},
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "\n",
            "Optimized Landmark Locations:\n",
            "  L0: [-48.11741249  31.92467992]\n",
            "  L1: [-80.92811295  53.95372591]\n",
            "  L5: [-47.60339748 -19.97294509]\n",
            "  L6: [-17.70157972  66.35356579]\n"
          ]
        }
      ],
      "source": [
        "# Print optimized landmarks:\n",
        "print(\"\\nOptimized Landmark Locations:\")\n",
        "for j in [0, 1, 5, 6]: # Print specific landmarks like MATLAB example\n",
        "    if j in sorted_landmark_ids:\n",
        "        landmark_key = gtsam.symbol('L', j)\n",
        "        try:\n",
        "            p = result.atPoint2(landmark_key)\n",
        "            print(f\"  L{j}: {p}\")\n",
        "        except Exception as e:\n",
        "            print(f\"  L{j}: Not found in result ({e})\")\n",
        "    else:\n",
        "        print(f\"  L{j}: Not present in TD data.\")"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 44,
      "metadata": {},
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "\n",
            "Extracted 4091 final poses and 4 landmarks.\n"
          ]
        }
      ],
      "source": [
        "# Extract poses and landmarks for plotting\n",
        "poses_result = gtsam.utilities.allPose2s(result)\n",
        "landmarks_result = gtsam.utilities.extractPoint2(result)\n",
        "positions_result = np.array([poses_result.atPose2(key).translation() \n",
        "                             for key in range(M + 1)]) # Poses 0 to M\n",
        "\n",
        "# Also extract initial estimate poses (dead reckoning)\n",
        "poses_initial = gtsam.utilities.allPose2s(initial)\n",
        "positions_initial = np.array([poses_initial.atPose2(key).translation() \n",
        "                              for key in range(M + 1)])\n",
        "\n",
        "print(f\"\\nExtracted {positions_result.shape[0]} final poses and {landmarks_result.shape[0]} landmarks.\")"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 45,
      "metadata": {},
      "outputs": [
        {
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                      "bgcolor": "#E5ECF6",
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                    },
                    "scene": {
                      "xaxis": {
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                        "gridwidth": 2,
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                      "yaxis": {
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                        "gridwidth": 2,
                        "linecolor": "white",
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                        "ticks": "",
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                      "zaxis": {
                        "backgroundcolor": "#E5ECF6",
                        "gridcolor": "white",
                        "gridwidth": 2,
                        "linecolor": "white",
                        "showbackground": true,
                        "ticks": "",
                        "zerolinecolor": "white"
                      }
                    },
                    "shapedefaults": {
                      "line": {
                        "color": "#2a3f5f"
                      }
                    },
                    "ternary": {
                      "aaxis": {
                        "gridcolor": "white",
                        "linecolor": "white",
                        "ticks": ""
                      },
                      "baxis": {
                        "gridcolor": "white",
                        "linecolor": "white",
                        "ticks": ""
                      },
                      "bgcolor": "#E5ECF6",
                      "caxis": {
                        "gridcolor": "white",
                        "linecolor": "white",
                        "ticks": ""
                      }
                    },
                    "title": {
                      "x": 0.05
                    },
                    "xaxis": {
                      "automargin": true,
                      "gridcolor": "white",
                      "linecolor": "white",
                      "ticks": "",
                      "title": {
                        "standoff": 15
                      },
                      "zerolinecolor": "white",
                      "zerolinewidth": 2
                    },
                    "yaxis": {
                      "automargin": true,
                      "gridcolor": "white",
                      "linecolor": "white",
                      "ticks": "",
                      "title": {
                        "standoff": 15
                      },
                      "zerolinecolor": "white",
                      "zerolinewidth": 2
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                  }
                },
                "title": {
                  "text": "Plaza2 Batch SLAM Result"
                },
                "xaxis": {
                  "anchor": "y",
                  "domain": [
                    0,
                    1
                  ],
                  "title": {
                    "text": "X (m)"
                  }
                },
                "yaxis": {
                  "anchor": "x",
                  "domain": [
                    0,
                    1
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                  "scaleanchor": "x",
                  "scaleratio": 1,
                  "title": {
                    "text": "Y (m)"
                  }
                }
              }
            }
          },
          "metadata": {},
          "output_type": "display_data"
        }
      ],
      "source": [
        "# Plot using Plotly (similar to iSAM example)\n",
        "fig = px.line(x=positions_initial[:,0], y=positions_initial[:,1], title='Plaza2 Batch SLAM Result')\n",
        "fig.data[0].name = 'Initial (Odometry)'\n",
        "fig.data[0].showlegend = True\n",
        "fig.data[0].line.color = 'orange'\n",
        "fig.data[0].line.dash = 'dash'\n",
        "\n",
        "fig.add_scatter(x=positions_result[:,0], y=positions_result[:,1], mode='lines', \n",
        "                line=dict(color='black'), name='Optimized Path')\n",
        "\n",
        "fig.add_scatter(x=landmarks_result[:,0], y=landmarks_result[:,1], mode='markers', \n",
        "                marker=dict(color='red', symbol='star', size=8), name='Landmarks')\n",
        "\n",
        "# Configure layout\n",
        "fig.update_layout(margin=dict(l=20, r=20, t=40, b=20), \n",
        "                  legend=dict(yanchor=\"top\", y=0.99, xanchor=\"left\", x=0.01),\n",
        "                  xaxis_title=\"X (m)\", yaxis_title=\"Y (m)\")\n",
        "fig.update_yaxes(scaleanchor=\"x\", scaleratio=1) # Ensure aspect ratio is 1:1\n",
        "fig.show()"
      ]
    }
  ],
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    "kernelspec": {
      "display_name": "py312",
      "language": "python",
      "name": "python3"
    },
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      "pygments_lexer": "ipython3",
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